Title: Global optimisation procedures for solving systems of Hölder equations-inequations

Authors: Djaouida Guettal; Mohamed Rahal

Addresses: Laboratory of Fundamental and Numerical Mathematics, LMFN, Department of Mathematics, Ferhat Abbas, Sétif 1 University, Sétif, 19000, Algeria ' Laboratory of Fundamental and Numerical Mathematics, LMFN, Department of Mathematics, Ferhat Abbas, Sétif 1 University, Sétif, 19000, Algeria

Abstract: In this paper, Shubert-Piyavskii's algorithm (SPA) proposed for solving problems of global optimisation with Lipschitz data is extended to the class of Hölder global optimisation problems with several variables. It can be applied to solving systems of Hölder equations-inequations over a compact set of Rⁿ, by transforming the original systems into an equivalent Hölder global optimisation problem. We use a procedure for partitioning and eliminating hyper-surfaces without interest by constructing piecewise constant minorant functions, which depend on piecewise parabolic cone minorant functions. The proposed algorithm is proven to have a finite convergence to the global optimum. Computational results on several standard examples are given.

Keywords: global optimisation; covering methods; systems of equations-inequations; multivariate Hölder functions; Shubert-Piyavskii's algorithm.

DOI: 10.1504/IJCSM.2023.131457

International Journal of Computing Science and Mathematics, 2023 Vol.17 No.3, pp.266 - 275

Accepted: 13 Sep 2022
Published online: 13 Jun 2023 *

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